Airfoil profile for a turbine nozzle

ABSTRACT

An airfoil profile for a turbine nozzle of a gas turbine is provided. The turbine nozzle may include an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

TECHNICAL FIELD

This application relates to airfoils for a gas turbine and more particularly to an airfoil profile for a turbine nozzle of a gas turbine.

BACKGROUND

Turbines are machines that obtain rotational force by impulsive or reaction force using a flow of a compressible fluid such as steam or gas, and include a steam turbine using steam, a gas turbine using hot combustion gas, and so on.

The gas turbine includes a compressor, a combustor, and a turbine. The compressor includes an air inlet into which air is introduced, and a plurality of compressor vanes and a plurality of compressor blades which are alternately arranged in a compressor housing. The introduced air is compressed by the compressor vanes and the compressor blades while passing through an inside of the compressor.

The combustor supplies fuel to air compressed by the compressor and ignites a fuel-air mixture with an igniter to produce high-temperature and high-pressure combustion gas.

The turbine includes a plurality of turbine vanes and a plurality of turbine blades which are alternately arranged in a turbine housing. In addition, a rotor is arranged to pass through centers of the compressor, the combustor, the turbine, and an exhaust chamber.

The rotor is rotatably supported at both ends thereof by bearings. A plurality of disks are fixed to the rotor, and a plurality of blades are connected to each of the disks while a drive shaft of a generator is connected to an end of the exhaust chamber.

In a gas turbine, many system requirements should be met at each stage of the gas turbine to meet design goals. The design goals may include overall improved efficiency and airfoil loading capability. For example, a turbine nozzle airfoil profile should achieve thermal and mechanical operating requirements for that particular stage. There is thus a desire for an improved turbine nozzle airfoil profile for use in a turbine and the like.

SUMMARY

Aspects of one or more exemplary embodiments provide a unique airfoil profile for the nozzles of a turbine stage capable of enhancing aeromechanics and reducing thermal and mechanical stresses.

Additional aspects will be set forth in part in the description which follows and, in part, will become apparent from the description, or may be learned by practice of the exemplary embodiments.

According to an aspect of an exemplary embodiment, there is provided a turbine nozzle including: an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

The airfoil shape may lie within an envelope of +1-0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

The X and Y coordinate values are scalable as a function of a same constant or number, and a set of corresponding nominal Z coordinate values are scalable as a function of the same constant or number to provide at least one of a scaled up or a scaled down airfoil.

The airfoil shape may include a leaned airfoil section to reduce a secondary flow effect.

The turbine nozzle may further include a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.

According to an aspect of another exemplary embodiment, there is provided a turbine including: a turbine nozzle extending from a platform to an end wall and having an airfoil-shaped cross section having a leading edge, a trailing edge, and a pressure side and a suction side each of which extends from the leading edge to the trailing edge, wherein the turbine nozzle may include an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

According to an aspect of another exemplary embodiment, there is provided a gas turbine including: a compressor configured to compress air; a combustor configured to mix compressed air supplied from the compressor with fuel for combustion; and a turbine including a plurality of turbine nozzles and a plurality of turbine blades rotated by combustion gas to generate power, wherein each of the turbine nozzles extending from a platform to an end wall and having an airfoil-shaped cross section having a leading edge, a trailing edge, and a pressure side and a suction side each of which extends from the leading edge to the trailing edge, and wherein the turbine nozzle may include an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects will become more apparent from the following description of the exemplary embodiments with reference to the accompanying drawings, in which:

FIG. 1 is a partially cutaway perspective view illustrating a gas turbine according to an exemplary embodiment;

FIG. 2 is a cross-sectional view illustrating a schematic structure of the gas turbine according to the exemplary embodiment;

FIG. 3 is a schematic diagram of a turbine according to an exemplary embodiment;

FIG. 4 is an aft view of a turbine nozzle including an airfoil according to an exemplary embodiment;

FIG. 5 is a forward view of a turbine nozzle including an airfoil according to an exemplary embodiment; and

FIG. 6 is an airfoil shape including a leaned airfoil section according to an exemplary embodiment.

DETAILED DESCRIPTION

Various modifications and various embodiments will be described below in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the disclosure. It should be understood, however, that the various embodiments are not for limiting the scope of the disclosure to the specific embodiment, but they should be interpreted to include all modifications, equivalents, and alternatives of the embodiments included within the spirit and scope disclosed herein.

Hereinafter, exemplary embodiments will be described in detail with reference to the accompanying drawings. Throughout the disclosure, like reference numerals refer to like parts throughout the various figures and exemplary embodiments. In certain embodiments, a detailed description of functions and configurations well known in the art may be omitted to avoid obscuring appreciation of the disclosure by a person of ordinary skill in the art. For the same reason, some components may be exaggerated, omitted, or schematically illustrated in the accompanying drawings.

FIG. 1 is a partially cutaway perspective view illustrating a gas turbine according to an exemplary embodiment. FIG. 2 is a cross-sectional view illustrating a schematic structure of the gas turbine according to the exemplary embodiment.

Referring to FIGS. 1 and 2, the gas turbine 1000 may include a compressor 1100, a combustor 1200, and a turbine 1300. Based on a flow direction of gas (e.g., compressed air or combustion gas), the compressor 1100 is disposed at an upstream side of the gas turbine 1000, and the turbine 1300 is disposed at a downstream side of the gas turbine 1000. The combustor 1200 is disposed between the compressor 1100 and the turbine 1300.

The compressor 1100 includes compressor vanes 1120 and compressor rotors in a compressor housing. The turbine 1300 includes turbine vane 1320 and turbine rotors in a turbine housing. The compressor vanes 1120 and the compressor rotors are arranged in a multi-stage arrangement along the flow direction of compressed air. The turbine vanes 1320 and the turbine rotors are arranged in a multi-stage arrangement along the flow direction of combustion gas. The compressor 1100 is designed such that an internal space is gradually decreased in size from a front stage to a rear stage so that air drawn into the compressor 1100 can be compressed. On the contrary, the turbine 1300 is designed such that an internal space is gradually increased in size from a front stage to a rear stage so that combustion gas received from the combustor 1200 can expand.

A torque tube for transmitting a rotational torque generated by the turbine 1300 to the compressor 1100 is disposed between a compressor rotor that is located at the rearmost stage of the compressor 1100 and a turbine rotor that is located at the foremost stage of the turbine 1300. FIG. 2 illustrates a case in which the torque tube includes multiple torque tube disks arranged in a three-stage arrangement, but it is understood that this is only an example and other exemplary embodiments are not limited thereto. For example, the torque tube may include multiple torque tube disks arranged in an arrangement of equal to or greater than four stages or an arrangement of equal to or less than two stages.

Each of the compressor rotors includes a compressor rotor disk and a compressor blade 1110 fastened to the compressor disk. That is, the compressor 1100 includes a plurality of compressor rotor disks, and respective compressor rotor disks are coupled to each other by a tie rod to prevent axial separation in an axial direction. The compressor rotor disks are arranged in the axial direction with the tie rod extending through centers of the compressor disks. Adjacent compressor rotor disks are arranged such that opposing surfaces thereof are in tight contact with each other by being tightly fastened by the tie rod so that the adjacent compressor rotor disks cannot rotate relative to each other. Each of the compressor rotor disks has a plurality of compressor blades 1110 radially coupled to an outer circumferential surface thereof.

The compressor blades 1110 (or referred to as buckets) are radially coupled to an outer circumferential surface of each of the compressor rotor disks in a row. The compressor vanes 1120 (or referred to as nozzles) are provided on an inner circumferential surface of the compressor housing in an annular row in each stage, and rows of the compressor vanes 1120 are arranged between rows of the compressor blades 1110. While the compressor disks rotate along with a rotation of the tie rod, the compressor vanes 1120 fixed to the housing do not rotate. The compressor vanes 1120 guide the flow of compressed air moved from front-stage compressor blades to rear-stage compressor blades.

The tie rod is disposed to pass through centers of the plurality of compressor rotor disks and turbine rotor disks. One end of the tie rod is fastened to a compressor disk located at the foremost stage of the compressor 1100, and the other end thereof is fastened in the torque tube by a fastening nut.

It is understood that the tie rod is not limited to the example illustrated in FIG. 2, and may be changed or vary according to one or more other exemplary embodiments. For example, a single tie rod may be disposed to pass through the centers of the rotor disks, a plurality of tie rods may be arranged circumferentially, or a combination thereof may be used.

Also, a deswirler serving as a guide vane may be provided in the compressor 1100 to adjust an actual inflow angle of the fluid entering into an inlet of the combustor 1200 to a designed inflow angle.

The combustor 1200 mixes the introduced compressed air with fuel, burns a fuel-air mixture to produce high-temperature and high-pressure combustion gas with high energy, and increases the temperature of the combustion gas to a temperature at which the combustor and the turbine components are able to withstand an isobaric combustion process.

A plurality of combustors constituting the combustor 1200 of the gas turbine may be arranged in the housing in a form of a cell. The combustor 1200 may include a plurality of chambers 1210 and fuel nozzle modules 1220 arranged annually.

The high-temperature and high-pressure combustion gas supplied from the combustor 1200 flows into the turbine 1300 and expands while passing through the inside of the turbine 1300, thereby applying an impulsive force or reaction force to the turbine blades 1310 to generate a rotational torque. A portion of the rotational torque is transmitted to the compressor via the torque tube, and a remaining portion which is an excessive torque is used to drive a generator to produce power.

The turbine 1300 basically has a structure similar to the compressor 1100. That is, the turbine 1300 may include a plurality of turbine rotors similar to the compressor rotors, and each of the turbine rotor may include a turbine rotor disk and a turbine blade 1310 fastened to the turbine rotor disk. A plurality of turbine blades 1310 (or referred to as buckets) are radially disposed. A plurality of turbine vanes 1320 (or referred to as nozzles) are fixedly arranged on an inner circumferential surface of the turbine housing in an annular row in each stage, and rows of the turbine vanes 1320 are arranged between rows of the turbine blades 1310. The turbine vanes 1320 guide the flow direction of combustion gas passing through the turbine blades 1310.

FIG. 3 is a schematic diagram of the turbine 1300 according to an exemplary embodiment. FIG. 4 is an aft view of a turbine nozzle including an airfoil according to an exemplary embodiment. FIG. 5 is a forward view of a turbine nozzle including an airfoil according to an exemplary embodiment.

Referring to FIG. 3, the turbine 1300 may include a plurality of turbine stages employing a plurality of nozzles and a plurality of buckets. For example, a first stage comprises a plurality of circumferentially spaced nozzles 20 and buckets 10. The nozzles are circumferentially spaced one from the other and fixed about the axis of the rotor. The first stage buckets 10 are mounted on the turbine rotor 17. A second stage of the turbine 1300 includes a plurality of circumferentially spaced nozzles 26 and buckets 16 mounted on the rotor 17. A third stage of the turbine 1300 includes a plurality of circumferentially spaced nozzles 32 and buckets 22 mounted on rotor 17. Although three stages are illustrated in FIG. 3, it is to be understood that any number of stages may be used.

Referring to FIGS. 4 and 5, the turbine nozzle 1320 according to the exemplary embodiment includes an airfoil extending from a platform 1340 to an end wall 1342. The turbine vane airfoil 1330 has an airfoil-shaped cross section having a leading edge 1331, a trailing edge 1332, a pressure side 1333, and a suction side 1334. The pressure side 1333 and the suction side 1334 are formed to extend from the leading edge 1331 to the trailing edge 1332.

The airfoil shape may be defined by a loci of points in space that meet stage design requirements. These points are unique and specific to the system. The list of X, Y, and Z coordinates for the airfoil, which are included as Table 1, has been optimized for stage efficiency, aerodynamic efficiency, and thermal and mechanical life requirements. In one exemplary embodiment, the points may be arrived at by iteration between aerodynamic and mechanical design optimization. Accordingly, these are the only loci of points that allow the gas turbine to run at the most efficient, safe and smooth manner.

Referring to FIGS. 4 and 5, the airfoil shape of the exemplary embodiment is defined by a unique set or loci of points in space that may be delineated. As shown in Table 1, the loci that defines the shape of the airfoil may include a set of approximately 1,440 points with X, Y and Z coordinates. The X, Y and Z coordinates, which represent the airfoil shape, are created in a coordinate system which is defined relative to the cold rotor centerline axis of the gas turbine (i.e., X coordinate axis). The origin of the coordinate system on the cold rotor centerline axis is defined as X=0.0, Y=0.0 and Z=0.0. For example, the coordinate system is set relative to the airfoil and is fully defined by points A, B and C. Points A and B are both located 41.650 inches above the cold rotor centerline axis. Point A lies at an intersection of the airfoil mean camber line and the leading-edge airfoil surface. Point B lies at an intersection of the airfoil mean camber line and the trailing-edge airfoil surface. Point C is located 46.100 inches above the cold rotor centerline axis and lies at the intersection of the airfoil mean camber line and the airfoil trailing-edge surface. Here, a coordinate system origin is located at point A. Points A and B define the positive X-axis. Points A, B and C define the positive X-Z plane. The Y-axis is then defined using the right-hand rule methodology. The coordinate values for the X, Y and Z coordinates are set forth in inches in Table 1, although other units of dimensions may be used if the values are appropriately converted.

The Cartesian coordinate system of X, Y and Z values given in Table 1 below defines the shape of the airfoil according to an exemplary embodiment. More specifically, the shape of the airfoil is defined by the cloud of points listed such that airfoil could be constructed by defining approximately smooth sheet surfaces through the listed points. As one of ordinary skill in the art will appreciate, Table 1 values are generated and shown to three decimal places for determining the profile of airfoil. All of the 1440 points represent a nominal cold or room temperature shape of the airfoil. It will be appreciated that as the nozzle heats up in operation, mechanical loading and temperature will cause a change in X, Y and Z coordinates. Accordingly, values for the airfoil shape given in Table 1 represent ambient, non-operating or non-hot conditions.

The coordinate values set forth in Table 1 below are for a cold condition of the turbine nozzle (e.g., non-rotating state and at room temperature). Further, the coordinate values set forth in Table 1 are for an uncoated nominal three-dimensional (3D) shape of the turbine nozzle. In some aspects, a coating (e.g., corrosion protective coating) may be applied to the turbine nozzle. The coating thickness may up to about 0.010 inches thick.

Further, the turbine nozzle 1320 may be fabricated using a variety of manufacturing techniques, such as forging, casting, milling, electro-chemical machining, electric-discharge machining, and the like. As such, the turbine nozzle may have a series of manufacturing tolerances for the position, profile, twist, and chord that can cause the turbine nozzle to vary from the nominal 3D shape defined by the coordinate values set forth in Table 1. This manufacturing tolerance may be, for example, +1-0.120 inches in a direction away from any of the coordinate values of Table 1 without departing from the scope of the subject matter described herein.

In addition to manufacturing tolerances affecting the overall size of the turbine nozzle, it is also possible to scale the airfoil to a larger or smaller airfoil size. In order to maintain the benefits of this 3D shape, in terms of stiffness and stress, it is necessary to scale the turbine nozzle uniformly in the X, Y, and Z directions.

The Table 1 values are generated and shown for determining the profile of the airfoil. There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/−typical manufacturing tolerances, i.e., +/−values, including any coating thicknesses, are additive to the X, Y and Z values given in Table 1 below.

TABLE 1 X Y Z Section 1 Point 1 5.994 −0.345 −0.677 Point 2 5.903 −0.290 −0.673 Point 3 5.786 −0.323 −0.676 Point 4 5.669 −0.356 −0.678 Point 5 5.551 −0.388 −0.680 Point 6 5.434 −0.420 −0.683 Point 7 5.316 −0.451 −0.685 Point 8 5.199 −0.481 −0.687 Point 9 5.081 −0.510 −0.689 Point 10 4.962 −0.538 −0.692 Point 11 4.844 −0.565 −0.694 Point 12 4.725 −0.590 −0.695 Point 13 4.606 −0.614 −0.697 Point 14 4.486 −0.636 −0.699 Point 15 4.366 −0.656 −0.700 Point 16 4.246 −0.674 −0.702 Point 17 4.125 −0.690 −0.703 Point 18 4.005 −0.703 −0.704 Point 19 3.884 −0.715 −0.705 Point 20 3.762 −0.724 −0.705 Point 21 3.641 −0.730 −0.706 Point 22 3.519 −0.734 −0.706 Point 23 3.398 −0.735 −0.706 Point 24 3.276 −0.734 −0.706 Point 25 3.155 −0.729 −0.706 Point 26 3.034 −0.722 −0.705 Point 27 2.912 −0.711 −0.704 Point 28 2.792 −0.698 −0.703 Point 29 2.671 −0.682 −0.702 Point 30 2.551 −0.663 −0.701 Point 31 2.431 −0.641 −0.699 Point 32 2.312 −0.617 −0.697 Point 33 2.194 −0.589 −0.695 Point 34 2.076 −0.559 −0.693 Point 35 1.959 −0.527 −0.691 Point 36 1.843 −0.492 −0.688 Point 37 1.727 −0.455 −0.685 Point 38 1.612 −0.415 −0.682 Point 39 1.498 −0.374 −0.679 Point 40 1.384 −0.331 −0.676 Point 41 1.271 −0.286 −0.673 Point 42 1.158 −0.241 −0.670 Point 43 1.046 −0.194 −0.666 Point 44 0.934 −0.146 −0.663 Point 45 0.823 −0.098 −0.659 Point 46 0.711 −0.051 −0.656 Point 47 0.598 −0.005 −0.652 Point 48 0.484 0.038 −0.649 Point 49 0.369 0.075 −0.646 Point 50 0.250 0.101 −0.644 Point 51 0.129 0.103 −0.644 Point 52 0.013 0.068 −0.647 Point 53 −0.092 0.007 −0.651 Point 54 −0.177 −0.078 −0.658 Point 55 −0.239 −0.183 −0.665 Point 56 −0.285 −0.295 −0.674 Point 57 −0.318 −0.411 −0.682 Point 58 −0.341 −0.530 −0.691 Point 59 −0.355 −0.651 −0.700 Point 60 −0.357 −0.772 −0.709 Point 61 −0.349 −0.893 −0.718 Point 62 −0.331 −1.013 −0.727 Point 63 −0.303 −1.131 −0.735 Point 64 −0.264 −1.246 −0.744 Point 65 −0.214 −1.356 −0.752 Point 66 −0.153 −1.460 −0.760 Point 67 −0.080 −1.557 −0.767 Point 68 0.004 −1.645 −0.773 Point 69 0.097 −1.723 −0.779 Point 70 0.198 −1.791 −0.784 Point 71 0.305 −1.848 −0.788 Point 72 0.417 −1.894 −0.792 Point 73 0.533 −1.932 −0.795 Point 74 0.651 −1.960 −0.797 Point 75 0.771 −1.981 −0.798 Point 76 0.892 −1.996 −0.799 Point 77 1.013 −2.003 −0.800 Point 78 1.134 −2.006 −0.800 Point 79 1.256 −2.004 −0.800 Point 80 1.377 −1.997 −0.799 Point 81 1.498 −1.987 −0.799 Point 82 1.619 −1.973 −0.798 Point 83 1.740 −1.956 −0.796 Point 84 1.860 −1.937 −0.795 Point 85 1.979 −1.915 −0.793 Point 86 2.098 −1.891 −0.792 Point 87 2.217 −1.865 −0.790 Point 88 2.335 −1.837 −0.788 Point 89 2.453 −1.807 −0.785 Point 90 2.571 −1.776 −0.783 Point 91 2.688 −1.743 −0.781 Point 92 2.804 −1.709 −0.778 Point 93 2.921 −1.674 −0.776 Point 94 3.037 −1.637 −0.773 Point 95 3.152 −1.600 −0.770 Point 96 3.267 −1.561 −0.767 Point 97 3.382 −1.522 −0.764 Point 98 3.497 −1.481 −0.761 Point 99 3.611 −1.440 −0.758 Point 100 3.726 −1.398 −0.755 Point 101 3.839 −1.356 −0.752 Point 102 3.953 −1.312 −0.749 Point 103 4.066 −1.268 −0.746 Point 104 4.179 −1.224 −0.742 Point 105 4.292 −1.179 −0.739 Point 106 4.405 −1.133 −0.736 Point 107 4.517 −1.087 −0.732 Point 108 4.629 −1.040 −0.729 Point 109 4.741 −0.993 −0.725 Point 110 4.853 −0.945 −0.722 Point 111 4.965 −0.897 −0.718 Point 112 5.076 −0.849 −0.715 Point 113 5.187 −0.800 −0.711 Point 114 5.299 −0.751 −0.707 Point 115 5.409 −0.701 −0.704 Point 116 5.520 −0.651 −0.700 Point 117 5.631 −0.601 −0.696 Point 118 5.741 −0.550 −0.692 Point 119 5.852 −0.499 −0.689 Point 120 5.961 −0.447 −0.685 Section 2 Point 1 6.172 −0.042 −0.103 Point 2 6.078 0.005 −0.100 Point 3 5.960 −0.028 −0.102 Point 4 5.841 −0.062 −0.105 Point 5 5.722 −0.095 −0.107 Point 6 5.603 −0.127 −0.110 Point 7 5.484 −0.159 −0.112 Point 8 5.365 −0.190 −0.114 Point 9 5.245 −0.220 −0.117 Point 10 5.125 −0.249 −0.119 Point 11 5.005 −0.277 −0.121 Point 12 4.885 −0.304 −0.123 Point 13 4.765 −0.330 −0.125 Point 14 4.644 −0.355 −0.127 Point 15 4.523 −0.378 −0.128 Point 16 4.401 −0.400 −0.130 Point 17 4.280 −0.421 −0.131 Point 18 4.158 −0.440 −0.133 Point 19 4.036 −0.458 −0.134 Point 20 3.914 −0.474 −0.135 Point 21 3.791 −0.489 −0.136 Point 22 3.669 −0.501 −0.137 Point 23 3.546 −0.512 −0.138 Point 24 3.423 −0.521 −0.139 Point 25 3.300 −0.527 −0.139 Point 26 3.176 −0.532 −0.140 Point 27 3.053 −0.534 −0.140 Point 28 2.930 −0.534 −0.140 Point 29 2.807 −0.532 −0.140 Point 30 2.683 −0.527 −0.139 Point 31 2.560 −0.520 −0.139 Point 32 2.437 −0.510 −0.138 Point 33 2.315 −0.498 −0.137 Point 34 2.192 −0.482 −0.136 Point 35 2.070 −0.464 −0.135 Point 36 1.949 −0.443 −0.133 Point 37 1.828 −0.420 −0.131 Point 38 1.707 −0.393 −0.129 Point 39 1.588 −0.364 −0.127 Point 40 1.468 −0.332 −0.125 Point 41 1.350 −0.298 −0.122 Point 42 1.233 −0.261 −0.120 Point 43 1.116 −0.221 −0.117 Point 44 1.000 −0.180 −0.114 Point 45 0.884 −0.137 −0.110 Point 46 0.769 −0.093 −0.107 Point 47 0.654 −0.050 −0.104 Point 48 0.537 −0.008 −0.101 Point 49 0.420 0.029 −0.098 Point 50 0.299 0.054 −0.096 Point 51 0.176 0.060 −0.096 Point 52 0.056 0.034 −0.098 Point 53 −0.053 −0.022 −0.102 Point 54 −0.139 −0.110 −0.108 Point 55 −0.199 −0.217 −0.116 Point 56 −0.242 −0.332 −0.125 Point 57 −0.271 −0.451 −0.134 Point 58 −0.289 −0.573 −0.143 Point 59 −0.296 −0.696 −0.152 Point 60 −0.293 −0.819 −0.161 Point 61 −0.280 −0.941 −0.170 Point 62 −0.257 −1.062 −0.179 Point 63 −0.224 −1.180 −0.188 Point 64 −0.179 −1.294 −0.196 Point 65 −0.123 −1.404 −0.204 Point 66 −0.054 −1.506 −0.212 Point 67 0.026 −1.599 −0.219 Point 68 0.117 −1.682 −0.225 Point 69 0.218 −1.753 −0.230 Point 70 0.326 −1.812 −0.234 Point 71 0.440 −1.858 −0.238 Point 72 0.558 −1.893 −0.240 Point 73 0.679 −1.918 −0.242 Point 74 0.801 −1.934 −0.243 Point 75 0.924 −1.942 −0.244 Point 76 1.047 −1.943 −0.244 Point 77 1.171 −1.939 −0.244 Point 78 1.294 −1.929 −0.243 Point 79 1.416 −1.915 −0.242 Point 80 1.538 −1.897 −0.241 Point 81 1.660 −1.875 −0.239 Point 82 1.780 −1.851 −0.237 Point 83 1.901 −1.824 −0.235 Point 84 2.021 −1.795 −0.233 Point 85 2.140 −1.764 −0.231 Point 86 2.259 −1.731 −0.228 Point 87 2.377 −1.696 −0.226 Point 88 2.495 −1.660 −0.223 Point 89 2.612 −1.623 −0.220 Point 90 2.729 −1.584 −0.217 Point 91 2.846 −1.544 −0.214 Point 92 2.962 −1.503 −0.211 Point 93 3.078 −1.461 −0.208 Point 94 3.194 −1.418 −0.205 Point 95 3.309 −1.374 −0.202 Point 96 3.424 −1.330 −0.199 Point 97 3.539 −1.285 −0.195 Point 98 3.653 −1.239 −0.192 Point 99 3.767 −1.193 −0.189 Point 100 3.882 −1.146 −0.185 Point 101 3.995 −1.099 −0.182 Point 102 4.109 −1.051 −0.178 Point 103 4.222 −1.003 −0.174 Point 104 4.336 −0.955 −0.171 Point 105 4.449 −0.906 −0.167 Point 106 4.562 −0.856 −0.164 Point 107 4.675 −0.807 −0.160 Point 108 4.787 −0.757 −0.156 Point 109 4.900 −0.707 −0.153 Point 110 5.012 −0.656 −0.149 Point 111 5.124 −0.605 −0.145 Point 112 5.237 −0.554 −0.141 Point 113 5.349 −0.503 −0.137 Point 114 5.461 −0.451 −0.134 Point 115 5.573 −0.399 −0.130 Point 116 5.684 −0.347 −0.126 Point 117 5.796 −0.295 −0.122 Point 118 5.908 −0.243 −0.118 Point 119 6.019 −0.190 −0.114 Point 120 6.130 −0.139 −0.111 Section 3 Point 1 6.283 0.139 0.461 Point 2 6.239 0.043 0.454 Point 3 6.283 0.139 0.461 Point 4 6.185 0.179 0.464 Point 5 6.066 0.143 0.462 Point 6 5.946 0.109 0.459 Point 7 5.826 0.076 0.457 Point 8 5.706 0.044 0.454 Point 9 5.585 0.012 0.452 Point 10 5.464 −0.019 0.450 Point 11 5.344 −0.049 0.448 Point 12 5.222 −0.079 0.445 Point 13 5.101 −0.108 0.443 Point 14 4.979 −0.135 0.441 Point 15 4.858 −0.162 0.439 Point 16 4.736 −0.188 0.437 Point 17 4.614 −0.213 0.435 Point 18 4.491 −0.237 0.434 Point 19 4.369 −0.260 0.432 Point 20 4.246 −0.282 0.430 Point 21 4.123 −0.303 0.429 Point 22 4.000 −0.323 0.427 Point 23 3.877 −0.341 0.426 Point 24 3.753 −0.358 0.425 Point 25 3.630 −0.374 0.424 Point 26 3.506 −0.389 0.422 Point 27 3.382 −0.402 0.422 Point 28 3.257 −0.413 0.421 Point 29 3.133 −0.423 0.420 Point 30 3.009 −0.431 0.419 Point 31 2.884 −0.437 0.419 Point 32 2.760 −0.441 0.419 Point 33 2.635 −0.444 0.418 Point 34 2.510 −0.444 0.418 Point 35 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Point 106 4.431 −0.797 0.392 Point 107 4.544 −0.746 0.396 Point 108 4.658 −0.694 0.400 Point 109 4.771 −0.643 0.404 Point 110 4.885 −0.591 0.408 Point 111 4.998 −0.539 0.411 Point 112 5.111 −0.487 0.415 Point 113 5.224 −0.434 0.419 Point 114 5.337 −0.382 0.423 Point 115 5.450 −0.329 0.427 Point 116 5.563 −0.276 0.431 Point 117 5.676 −0.223 0.435 Point 118 5.789 −0.170 0.439 Point 119 5.902 −0.117 0.443 Point 120 6.014 −0.064 0.446 Section 4 Point 1 6.366 0.218 1.019 Point 2 6.267 0.257 1.022 Point 3 6.146 0.222 1.019 Point 4 6.025 0.188 1.017 Point 5 5.903 0.154 1.014 Point 6 5.781 0.122 1.012 Point 7 5.659 0.090 1.009 Point 8 5.537 0.059 1.007 Point 9 5.414 0.029 1.005 Point 10 5.292 0.000 1.003 Point 11 5.169 −0.029 1.001 Point 12 5.046 −0.057 0.999 Point 13 4.923 −0.084 0.997 Point 14 4.799 −0.110 0.995 Point 15 4.676 −0.135 0.993 Point 16 4.552 −0.159 0.991 Point 17 4.428 −0.183 0.989 Point 18 4.304 −0.205 0.988 Point 19 4.180 −0.227 0.986 Point 20 4.055 −0.247 0.984 Point 21 3.931 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3.101 −1.328 0.905 Point 93 3.218 −1.281 0.908 Point 94 3.334 −1.232 0.912 Point 95 3.450 −1.184 0.915 Point 96 3.567 −1.135 0.919 Point 97 3.682 −1.085 0.922 Point 98 3.798 −1.035 0.926 Point 99 3.914 −0.985 0.930 Point 100 4.029 −0.934 0.934 Point 101 4.144 −0.883 0.937 Point 102 4.259 −0.832 0.941 Point 103 4.374 −0.780 0.945 Point 104 4.489 −0.728 0.949 Point 105 4.604 −0.676 0.953 Point 106 4.719 −0.624 0.957 Point 107 4.833 −0.571 0.960 Point 108 4.948 −0.519 0.964 Point 109 5.062 −0.466 0.968 Point 110 5.177 −0.413 0.972 Point 111 5.291 −0.360 0.976 Point 112 5.405 −0.306 0.980 Point 113 5.519 −0.253 0.984 Point 114 5.634 −0.199 0.988 Point 115 5.748 −0.146 0.992 Point 116 5.862 −0.092 0.996 Point 117 5.976 −0.038 1.000 Point 118 6.090 0.015 1.004 Point 119 6.204 0.069 1.008 Point 120 6.318 0.123 1.012 Section 5 Point 1 6.459 0.245 1.572 Point 2 6.410 0.150 1.565 Point 3 6.459 0.245 1.572 Point 4 6.359 0.283 1.575 Point 5 6.236 0.248 1.573 Point 6 6.113 0.213 1.570 Point 7 5.990 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Point 114 5.486 −0.285 1.533 Point 115 5.602 −0.231 1.537 Point 116 5.717 −0.177 1.541 Point 117 5.833 −0.122 1.545 Point 118 5.948 −0.068 1.549 Point 119 6.063 −0.013 1.553 Point 120 6.179 0.041 1.557 Section 6 Point 1 6.563 0.239 2.123 Point 2 6.512 0.143 2.116 Point 3 6.563 0.239 2.123 Point 4 6.461 0.276 2.126 Point 5 6.337 0.240 2.123 Point 6 6.212 0.205 2.121 Point 7 6.088 0.171 2.118 Point 8 5.962 0.139 2.116 Point 9 5.837 0.106 2.114 Point 10 5.712 0.075 2.111 Point 11 5.586 0.044 2.109 Point 12 5.460 0.014 2.107 Point 13 5.334 −0.015 2.105 Point 14 5.208 −0.043 2.103 Point 15 5.082 −0.071 2.101 Point 16 4.955 −0.098 2.099 Point 17 4.829 −0.124 2.097 Point 18 4.702 −0.149 2.095 Point 19 4.575 −0.174 2.093 Point 20 4.448 −0.198 2.091 Point 21 4.321 −0.221 2.089 Point 22 4.193 −0.243 2.088 Point 23 4.066 −0.264 2.086 Point 24 3.938 −0.284 2.085 Point 25 3.810 −0.304 2.083 Point 26 3.682 −0.322 2.082 Point 27 3.554 −0.340 2.081 Point 28 3.426 −0.356 2.079 Point 29 3.297 −0.371 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2.028 Point 101 4.050 −1.002 2.032 Point 102 4.168 −0.949 2.036 Point 103 4.286 −0.895 2.040 Point 104 4.403 −0.842 2.043 Point 105 4.521 −0.788 2.047 Point 106 4.639 −0.734 2.051 Point 107 4.756 −0.680 2.055 Point 108 4.873 −0.626 2.059 Point 109 4.991 −0.571 2.063 Point 110 5.108 −0.517 2.068 Point 111 5.225 −0.462 2.072 Point 112 5.342 −0.407 2.076 Point 113 5.459 −0.353 2.080 Point 114 5.576 −0.298 2.084 Point 115 5.693 −0.243 2.088 Point 116 5.810 −0.188 2.092 Point 117 5.927 −0.132 2.096 Point 118 6.044 −0.077 2.100 Point 119 6.161 −0.022 2.104 Point 120 6.278 0.033 2.108 Section 7 Point 1 6.670 0.209 2.673 Point 2 6.566 0.246 2.675 Point 3 6.440 0.210 2.673 Point 4 6.314 0.175 2.670 Point 5 6.187 0.142 2.668 Point 6 6.061 0.109 2.665 Point 7 5.934 0.077 2.663 Point 8 5.807 0.046 2.661 Point 9 5.679 0.015 2.658 Point 10 5.552 −0.014 2.656 Point 11 5.424 −0.043 2.654 Point 12 5.296 −0.072 2.652 Point 13 5.168 −0.099 2.650 Point 14 5.040 −0.126 2.648 Point 15 4.911 −0.152 2.646 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88 2.992 −1.869 5.277 Point 89 3.120 −1.824 5.280 Point 90 3.248 −1.778 5.283 Point 91 3.376 −1.732 5.287 Point 92 3.503 −1.684 5.290 Point 93 3.630 −1.636 5.294 Point 94 3.757 −1.587 5.297 Point 95 3.883 −1.538 5.301 Point 96 4.010 −1.488 5.305 Point 97 4.136 −1.438 5.308 Point 98 4.262 −1.388 5.312 Point 99 4.389 −1.337 5.316 Point 100 4.515 −1.287 5.320 Point 101 4.640 −1.236 5.323 Point 102 4.766 −1.184 5.327 Point 103 4.892 −1.133 5.331 Point 104 5.018 −1.081 5.335 Point 105 5.143 −1.029 5.339 Point 106 5.269 −0.978 5.342 Point 107 5.395 −0.926 5.346 Point 108 5.520 −0.874 5.350 Point 109 5.646 −0.822 5.354 Point 110 5.771 −0.770 5.358 Point 111 5.896 −0.717 5.362 Point 112 6.022 −0.665 5.366 Point 113 6.147 −0.613 5.369 Point 114 6.273 −0.561 5.373 Point 115 6.398 −0.508 5.377 Point 116 6.524 −0.456 5.381 Point 117 6.649 −0.404 5.385 Point 118 6.774 −0.352 5.389 Point 119 6.900 −0.299 5.393 Point 120 7.025 −0.247 5.396

FIG. 6 illustrates an airfoil shape including a leaned airfoil section 1360 according to an exemplary embodiment. As the nozzles come into direct contact with the high-temperature and high-pressure combustion gas, a secondary flow occurs. That is, secondary flows are flow effects that occur after the high-temperature and high-pressure combustion gas path flow contacts the nozzles. The effects are not good as they negatively affect aerodynamic performance, causing turbulence in the flow path. Further, the turbulences may increase the heat transfer coefficients on the gas path surface which also increases heat transfer/metal temperature rise by increasing the heat transfer coefficient of the gas path surface. In order to reduce losses caused by the secondary flows, a newly designed airfoil shape is needed. According to the newly designed airfoil shape of the exemplary embodiment which includes a leaned airfoil section 1360 as illustrated in FIG. 6, it is possible to reduce the secondary flow effects aerodynamically by changing the shape/contour of the airfoil.

While one or more exemplary embodiments have been described with reference to the accompanying drawings, it is to be understood by those skilled in the art that various modifications and changes in form and details can be made therein without departing from the spirit and scope as defined by the appended claims. Therefore, the description of the exemplary embodiments should be construed in a descriptive sense only and not to limit the scope of the claims, and many alternatives, modifications, and variations will be apparent to those skilled in the art. 

What is claimed is:
 1. A turbine nozzle comprising: an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.
 2. The turbine nozzle according to claim 1, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 3. The turbine nozzle according to claim 1, wherein the X and Y coordinate values are scalable as a function of a same constant or number and a set of corresponding nominal Z coordinate values are scalable as a function of the same constant or number to provide at least one of a scaled up or a scaled down airfoil.
 4. The turbine nozzle according to claim 3, wherein the airfoil shape includes a leaned airfoil section to reduce a secondary flow effect.
 5. The turbine nozzle according to claim 1, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.
 6. A turbine comprising: a turbine nozzle extending from a platform to an end wall and having an airfoil-shaped cross section having a leading edge, a trailing edge, and a pressure side and a suction side each of which extends from the leading edge to the trailing edge, wherein the turbine nozzle comprises an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.
 7. The turbine according to claim 6, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 8. The turbine according to claim 6, wherein the X and Y coordinate values are scalable as a function of a same constant or number and a set of corresponding nominal Z coordinate values are scalable as a function of the same constant or number to provide at least one of a scaled up or a scaled down airfoil.
 9. The turbine according to claim 8, wherein the airfoil shape includes a leaned airfoil section to reduce a secondary flow effect.
 10. The turbine according to claim 6, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.
 11. A gas turbine comprising: a compressor configured to compress air; a combustor configured to mix compressed air supplied from the compressor with fuel for combustion to generate combustion gas; and a turbine comprising a plurality of turbine nozzles and a plurality of turbine blades rotated by the combustion gas to generate power, wherein each of the turbine nozzles extending from a platform to an end wall and having an airfoil-shaped cross section having a leading edge, a trailing edge, and a pressure side and a suction side each of which extends from the leading edge to the trailing edge, wherein the turbine nozzle comprises an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.
 12. The gas turbine according to claim 11, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 13. The turbine according to claim 11, wherein the X and Y coordinate values are scalable as a function of a same constant or number and a set of corresponding nominal Z coordinate values are scalable as a function of the same constant or number to provide at least one of a scaled up or a scaled down airfoil.
 14. The gas turbine according to claim 13, wherein the airfoil shape includes a leaned airfoil section to reduce a secondary flow effect.
 15. The gas turbine according to claim 11, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches. 